Motion Estimation in Ultrasonic Images
Motion estimation is often useful for recognition of patterns in the sequence of ultrasonic images [1-6]. In muscular-skeletal applications, motion estimation provides a powerful diagnostic tool for the identification of pathological abnormalities. The applications of tissue motion estimation to ultrasonic tissue characterization and blood flow images are two of the most promising areas of research in medical motion image analysis today. But motion estimation algorithms, which are appropriate for rigid body motions, are not optimal for soft tissue motions in ultrasonic images.
In fact, ultrasonic images are usually influenced by speckle patterns [7], which arise from the constructive and destructive interference of coherent echo signals and speckle de-correlation as well. Speckle pattern de-correlation can be induced by out-of-plane motion, non-uniform motion in sub-resolution scatters, non-uniformity in the ultrasound field and non-rigid tissue deformation.
Since the performance of speckle tracking algorithms usually depends on the stability of the speckle pattern, it often yields inaccurate motion estimates in regions where the speckle de-correlation is high.
To obtain better ultrasonic image analysis, Maurice and Bertrand proposed a Lagrange speckle model [2] for tissue motion estimation. Strintzis and Kokkinidis adopted a maximum likelihood estimation method [3] for the matching technique. Yeung et al. proposed a multilevel and motion model-based algorithm [4] and a deformable mesh-based algorithm [5] for motion tracking. The finite element analysis was employed in manipulating the irregular mesh elements in [5]. The experimental results illustrated that the deformable mesh was successful in tracking the non-rigid motion fields. Our proposed method is also based on tracking. Without establishing a concrete mesh, we adopted the proposed metamorphosis-based method to handle motion tracking with respected to some detected feature points. The tracking results are then refined by optimizing the image energy.
For solving the speckle de-correlation problem, it is necessary to utilize the a priori knowledge based on the physical properties of the tissue motion. A continuous smoothness constraint on the tissue motion field is usually adopted. This assumption is generally valid when the motion vectors are contained within a single moving or deforming object. Even at the boundaries of tissues with different properties, motion continuity is still valid provided that the stress is also continuous. This smoothness constraint can be imposed on a local neighborhood of motion estimates to explore the connectivity among the neighboring motion vectors.
In the last decade, the problem of estimating optical flow from a sequence of images has been studied extensively. These approaches may be broadly classified into optical-flow-based [8], block-based [9], and feature-based [10-13] techniques. Optical-flow-based estimation relies on
the instantaneous changes in the brightness value. Block-based methods assume that the motion field is piecewise translatory. Feature-based methods rely on extracting relevant features such as edges [10, 11], object boundaries [12, 13], etc., and establishing an inter-frame correspondence.
For object motion tracking, an active contour model [17, 18] is often adopted. For speedup and solving the problem of large displacement, a hierarchical method [14-16] is often adopted. A hierarchical method, either based on the optical flow method [14] or block based method [15, 16], adopts a course-to-fine strategy. A course result is first calculated, and a more accurate result is achieved by adjusting the estimated flow on each level of the hierarchy.
Considering the simplicity of the block-based methods and the reliability of the feature-based methods, we propose a simple method based on both feature-based and block-based concepts.
The proposed method combines the feature metamorphosis mechanism [20-23] and the energy-based block-matching algorithm. Fig. 1 shows the flow chart of the proposed algorithm.
In matching algorithms, features usually provide more reliable correspondence. Therefore, we used a multi-scale scheme to extract feature points from the ultrasonic image for matching instead of whole pixels to acquire a more accurate result and reduce computation in the unreliable non-feature points. A dense flow field is then generated from these feature correspondences using a sub-division morphing, adopted to accelerate the process. In order to get an accurate result, an energy-based block matching method is adopted to refine the optical flow field. Compared to the traditional methods, the proposed method improves the efficiency and is suitable for soft tissue analysis in ultrasonic image sequences.
Fig. 1. Flow chart of the proposed system.
Motion Estimation in Tagged MR Images
Myocardial ischemia is caused by locally reduced blood flow due to a stenosis or obstruction of arteries. For better understanding of cardiac mechanics, analysis of the myocardial deformation [26-31] could serve as an essential indicator, since an injured region of myocardium is less contractile and results in abnormal motion during contraction. It has also been recognized that detecting regions with abnormal contraction may be used to assess myocardial viability after myocardial infarction.
Noninvasive estimation of cardiac motion is of interest in order to interpret and predict the progression of heart diseases. Recent research and development has shown that cardiac MRI (magnetic resonance imaging) that can provide excellent images for anatomic as well as functional evaluation has become the most important technique in noninvasive imaging for cardiac diagnoses. However, although the MR images provide good spatial resolution, we can hardly observe the internal deformation and indicate the abnormal region with the naked eyes during the contraction of myocardial wall.
In the last decade, MR tagged imaging techniques have been proposed and continuously improved for better visualization in cardiac motion [32-34]. The MR tagged images are shown especially helpful for measuring the deformation of an in vivo heart. The generated tag patterns act as markers and distort due to the tissue motion. The added tag patterns show the internal deformation of myocardium in the MR images and provide useful quantitative information about the cardiac function of the underlying myocardium.
The tagging schemes use a set of RF pulses to place tag planes perpendicular to the imaging slice. SPAMM (spatial modulation of magnetization), which is introduced by Axel and Dougherty [33], is a technique for producing a regular grid tag pattern. Two sets of regular dark bands, which are orthogonal to each other, are generated by selective saturation. The tagged objects, which are textured by SPAMM, reduce the ambiguity associated with the aperture problem in motion estimation. However, the resulting tag pattern is time varying. Because the contrast of tags decays gradually due to the inherent T1 recovery of myocardial tissue, brightness of tags varies that makes the tracking procedure nontrivial.
In the traditional motion estimation algorithms [35], the basic assumption that the brightness of all material points is time invariant is violated since the tag patterns fade away over time. The traditional algorithms usually fail in tracking the tags with the decaying contrast. Hence, applications of motion estimation in MR tagged images require an additional modification.
To account for the decay, a variable brightness optical flow algorithm [36] was developed to estimate the displacement fields in tagged MR image sequences. The optical flow equation was slightly modified according to the brightness variation. The tagged MR imaging equation was used to provide an estimate of the material time derivatives. A similar algorithm [37] was also proposed to overcome the tag decay problem by pre-filtering the tagged images with a Laplacian kernel to reduce the intensity bias.
Some researches adopted the profile fitting techniques [38-40] to track the tag patterns. Tag profiles are simulated as a function of time based on the physics of MRI. The positions of tag points are first detected using the expected appearance according to the simulated tag profile. A template-matching algorithm can then be applied to locate the tag patterns and track the tag motion.
In some deformable model based approaches [41-47], the detected grid pattern aims to minimize the predefined energies. The energies are defined according to the a priori knowledge of the tracking contour. Usually, the sum of intensities is defined as the external energy to agree with the tag property, and an internal energy is defined to provide smoothness of the model.
After the tag lines were tracked, the displacement measurements are still sparse and are valid only along the tag lines. Interpolation is hence needed to reconstruct the dense displacement field.
In [46], a two-dimensional B-spline representation is adopted to evaluate the dense displacement fields. In [48-51], parametric displacement models are adopted to approximate the dense displacement fields from sparse displacement measurements.
However, in a variable brightness optical flow method, acquiring the MR parameters is complex, and errors in estimating the parameters may ruin the tracking results. Besides, since the intensity decay happens only in the tagged regions, the motion estimation algorithm requires knowledge indicating regions with variant or invariant brightness. This reference map is usually generated from previous optical flow estimates. Hence, accurate motion estimates are highly demanded since the legality in brightness compensation is depended on the accuracy of the motion estimation. The errors introduced from inaccurate motion estimates and invalid brightness compensations degrade the performance over time.
Since the MR tagged images are textured with tag patterns, a feature based approach is more practicable. A common approach is to identify the intersection points of tag lines as markers for establishing point correspondences. However, the decaying contrast of tag lines affects the performance of feature extraction. Another problem happens when locating the tag position since the tag lines are usually two pixels wide. More than one feature points are extracted for one intersection. Feature tracking is hence not suitable for tag data.
The same problems also exist in snake based approach. Since the tag width is usually two pixels width, the snake may choose either of these two pixels. Further, the external energy is usually defined as the image intensity according to the tag property. However, the external energy decays over time due to the tag decay problem, and the snake will be fully controlled by the internal energies. Additionally, since the tag lines are appeared periodically, adjacent snakes may attach to the same tag line during the deforming process without a prior knowledge. Hence, the energies must be carefully defined.
In this research, a modified deformable model was proposed to resolve the tag-tracking problem. The basic procedure of the proposed method mainly consists of five steps. First, the myocardium region of the left ventricle (LV) was segmented in each image with an automatic algorithm based on the intensity variance image. Second, the tag information was extracted by
applying a series of morphological operations. Third, the proposed spatio-temporal patterns were utilized to generate the initial displacement fields. Fourth, the defined tag line positions were iteratively refined with a modified deformable model using both the temporal and spatial information. Finally, the tag line correspondences were used to reconstruct the dense deformation fields for cardiac function assessment.
In the segmentation process, variance images are adopted to identify the object and background. In the tracking process, the closed images, tag profile images, and edge images are generated as the references to extract the tag information. Spatio-temporal slices are proposed and used to calculate the initial displacement fields, and these initial displacement fields help to place the tag lines in the appropriate positions for further adjustment. The tag lines are then deformed towards the real tag boundaries using the energy model defined according to the tag properties.
Both the temporal and spatial information cooperates to track the tag lines. Finally, for clinical assessment, the displacement fields and deformation fields are calculated to generate the strain maps for detecting abnormal regions. The architecture of the proposed algorithm can be illustrated as in Fig. 2.
Fig. 2. Flow chart of the proposed tag motion analysis algorithm.